Subject: [mg96988] Re: [mg96961] "Do What I Mean" - a suggestion for improving

From: DrMajorBob <btreat1 at austin.rr.com>

Date: Sun, 1 Mar 2009 04:55:49 -0500 (EST)

References: <200902281142.GAA16641@smc.vnet.net>

Reply-to: drmajorbob at bigfoot.com

Sorry, but most (maybe none) of that can be done. Point by point:
1) x/xy is NOT a syntax error, and it may be exactly what I mean. It's up
to a user to write what he means.
2) There are no "functions" in Mathematica; only rules. If you defined
f[x_Integer]:=x^2 and then tried to evaluate f[2.3] the first rule isn't
invoked because 2.3 doesn't fit the pattern, so Mathematica has no
opportunity to match it (since it DOESN'T match) and then TELL you it
doesn't match. This may be EXACTLY what I want and expect to happen, so it
would be a waste of time for Mathematica to flag this as an error every
time it occurs.
3) NIntegrate, for instance, can only work if all variables and parameters
are numeric, and you already get an error message if they're not.
Integrate, on the other hand, can work with symbolic variables and numeric
parameters. There are a lot of case-by-case situations. I don't see how
Mathematica could guess whether you've tried what you meant to try. It
only knows (sometimes) how successful it was.
4) When FindMinimum or NIntegrate or NDSolve has precision problems,
there's no way for Mathematica to know how to proceed. Sometimes you need
a new Method, other times a new WorkingPrecision, and often, you're simply
NOT going to integrate the thing you're trying to integrate, no matter
WHAT you do.
DWIM is impossible, even in theory.
Bobby
On Sat, 28 Feb 2009 05:42:20 -0600, David Bakin <davidbak at gmail.com> wrote:
> A few days ago I posted that Mathematica should have a "DWIM" feature -
> "Do
> What I Mean".
>
> In InterLisp, in the 80's, the DWIM facility was hooked into error
> messages,
> and when invoked on a user error would poke around on the stack and in
> the
> environment using some rules to describe common error situations and it
> would uncover user errors and offer to correct them. Many of the errors
> were simple spelling errors and it would correct a misspelled variable
> name
> if it found an unbound variable but a similarly spelled variable was
> bound
> in the environment.
>
> Mathematica could benefit from this, and in fact, we at mathgroup could
> supply the rules (and framework) as a useful group project.
>
> If some guru would write the framework - trapping error messages somehow,
> perhaps when they were written to the $Messages channel (by replacing the
> default $Messages channel with something that would hook into the DWIM
> function), or perhaps with some other hook like redefining Message[] -
> then
> the rest of us could supply rules for the common errors. Especially the
> common errors we see puzzling Mathematica newbies on this list.
>
> I would suggest that the rules provide messages, hopefully with
> hyperlinks
> to the documentation.
>
> A true DWIM might also offer to rewrite the current expression and try it
> again, but I don't know if that can be done given the hooks into
> Mathematica
> that are currently available.
>
> Some situations that could be addressed are:
>
> 1. User writes "xy" instead of "x y". Rule could inspect the expression
> under evaluation and find (unevaluated) symbols like "xy" of the form
> "<prefix><suffix>" where both "<prefix>" and "<suffix>" were either
> symbols
> used in the expression or symbols bound in the environment. Rule would
> explain the problem and offer to rewrite expression and try again.
>
> 2. Some expression using a user-defined function causes an error when
> evaluating, or doesn't evaluate. Looking at the function, a rule finds
> function calls where the function arguments' patterns include "_Integer"
> or
> similar but the arguments given to it are not integers. Rule points to
> documentation describing argument types required by the called function.
>
> 3. Similar to 2 above, but it finds function calls that do numeric
> evaluation only or are optimized for numeric evaluation but the arguments
> given to it are symbolic.
>
> 4. Result returned is machine precision very close to zero (that is,
> with large negative exponent), but an error message complained of
> singularity, or other ill-conditioning. Rule points to documentation
> explaining about machine precision, and/or singularity, and offers to
> retry
> the expression with more digits of precision, rewriting the expression to
> achieve this.
>
> Actually, now that I think of it, the DWIM facility needs also to be
> invoked
> by the user because some of these situations don't cause error messages,
> but
> only cause (wholly or partially) unevaluated expressions. So maybe the
> user
> could be trained to type a word, like "Explain[]" after he didn't get the
> result he wanted and the DWIM facility would look at the In[] and Out[]
> arrays to find out what he's been doing recently.
>
> I would be glad to contribute rules to the framework ... but I'm not yet
> up
> to writing the framework. Hopefully one of the gurus here will find this
> interesting (and possible) and provide a framework. Then the rest of us
> could contribute rules that would improve the Mathematica experience for
> all
> newcomers. (AES, I'm looking at you! :-) )
>
> -- David
>
--
DrMajorBob at bigfoot.com